Random walk
A random walk is a process where each value equals the previous value, plus drift in the version with a trend, plus an unpredictable shock — so the best forecast of the next value is simply the last one, adjusted for drift.
What it is
See it move
A share closed yesterday at €54.20, and the price has drifted upward by an average of €0.15 per trading day. Under a random walk with drift, the best forecast for tomorrow's close is simply €54.20 + €0.15 = €54.35, since the day-to-day shock itself is, by definition, unpredictable and assumed to average zero.
The formula
Variables
- Value in the current period
- Value in the previous period
- Drift (average change per period)
- Random shock (expected value 0)
States that the best forecast for the next period is simply the last observed value plus the series' average drift per period.
Check yourself
An index last closed at 120.0 points. Its historical average drift is +1.5 points per period. Under a random-walk-with-drift model, what is the best forecast for the next period's close?